M2 - 18 Hypothesis testing

Question 1

What are the two types of hypothesis? What is the difference, what are we actually testing?

Answer 1

Alternate Hypothesis (Ha)
- states something is, will, or has changed
- stated hypothesis in a study is normally the alternative hypothesis
Null Hypothesis (Ho)
- things remain the same or do not change
- what we are actually testing

Question 2

How do you accept a hypothesis? What is a hypothesis?

Answer 2

Binary
Is not a theory, but could become one if given supporting evidence
A falsifiable statement that describes a phenomenon, it is an educated guess or prediction between 2 variables

Question 3

What are the acceptable error rates?

Answer 3

a > 0.5 1 in 20 (standard in physiology and psychology)
a > 0.01 1 in 100 (more statistically rigorous, better physiology standard)
a > 0.001 1 in 1000 (typical new engineering standard)
a = 2.87 x 10^-7 1 in 3 million (standard for theoretical physics) 5 sigma

Question 4

What are the equations for both hypotheses?

Answer 4

Ha : u1 > u2
- population mean in greater than expected value
Ho : u1=u2
- population mean is equal to expected value

Question 5

Type 1 errors vs type 2 errors + examples and 2 ways to calculate?

Answer 5

Type 1 = rejection of a true null hypothesis
- you state something has changed when it did not
- fire alarm rings, but no fire
referred to as a (alpha), use alpha to get P value
Type 2 = failure to reject a null hypothesis
- something changed, but we failed to see it
- no fire alarm, there is fire
beta = chance of having type 2 error

Question 6

What is a P value

Answer 6

The probability of obtaining the observed results if the null hypothesis is true
A p-value below a predetermined threshold usually leads to a rejection of the null hypothesis